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Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p. Statement-2 : r is equivalent to ~(p ↔ ~q).

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".


Statement-1 :
r is equivalent to either q or p.


Statement-2 :
r is equivalent to ~(p ↔ ~q).

Grade:12

1 Answers

ronit bhatiya
14 Points
12 years ago

p : x is an irrational number
q : y is a transcendental number
r : x is a rational number iff y is a transcendental number
=> r : ~ p ↔ q
s1 : q or p
s2 : ~ (p↔~q)


p q ~p ~q r:~p↔q s1:q or p p↔~q s2:~(p↔~q)
T T F F F T F T
T F F T T T T F
F T T F T T T F
F F T T F F F T

Based upon above chart
s1 and r are not equivalent
s2 and r are not equivalent

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